A comprehensive evaluation method and system for longitudinal deformation of shield tunnels

Abstract

The invention relates to the technical field of tunnel engineering design, and discloses a comprehensive evaluation method and system for the longitudinal deformation of a shield tunnel. The method comprises the following steps: obtaining analytical calculation parameters of a target shield tunnel; constructing a first shield tunnel force calculation model based on the analytical calculation parameters of the target shield tunnel and analytical calculation parameters of a target shield soil to calculate the additional stress at the axis of the target shield tunnel; constructing a work equation for the additional stress at the axis of the target shield tunnel to obtain the total work done by the force on the target shield tunnel; constructing a second shield tunnel longitudinal deformation calculation model based on an energy method to obtain a longitudinal displacement field at the axis of the target shield tunnel; constructing a third shield lining performance nonlinear degradation model to obtain an evaluation index for the longitudinal deformation of the target shield tunnel; and evaluating the longitudinal deformation of the target shield tunnel based on the evaluation index. The method solves the problems of existing tunnel longitudinal deformation evaluation methods in that a single influencing factor is considered and the evaluation accuracy is poor.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnel engineering design, and in particular to a comprehensive evaluation method and system for longitudinal deformation of a shield tunnel. Background Art

[0002] With the rapid development of shield tunneling technology, the density of underground projects in coastal areas has increased significantly in recent years. However, the complex geological and hydrological conditions in these areas, particularly water-rich strata, pose significant challenges to underground engineering. These conditions make tunnels highly susceptible to disturbances, including seasonal water-level fluctuations and nearby construction activities, leading to excessive additional deformations. These deformations can trigger a range of related issues, such as segment cracking, water leakage, and joint openings, ultimately accelerating structural degradation. Given the increasing complexity of underground projects in coastal areas, evaluating the structural performance of shield tunnels and ensuring their long-term safety and reliability is crucial. Therefore, it is crucial to determine the longitudinal deformation of existing shield tunnels during construction to ensure that degradation of the shield tunnel lining is within a reasonable range, thereby ensuring the safety of existing shield tunnels during surrounding construction. Currently, theoretical analytical methods are more rapid, accurate, and convenient for researchers and engineers to determine the longitudinal deformation of existing shield tunnels caused by water-level fluctuations and surrounding construction, compared to numerical simulations, laboratory model tests, and field testing. However, these methods typically only consider the influencing factors in a single case, without further analysis of the changes in shield tunnel lining performance. It can be seen that the existing tunnel longitudinal deformation evaluation method has the problems of considering only a single influencing factor and poor evaluation accuracy. Summary of the Invention

[0003] The present invention provides a comprehensive evaluation method and system for shield tunnel longitudinal deformation, so as to solve the problems of existing tunnel longitudinal deformation evaluation methods in which only a single influencing factor is considered and the evaluation accuracy is poor.

[0004] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0005] In a first aspect, the present invention provides a comprehensive evaluation method for longitudinal deformation of a shield tunnel, comprising:

[0006] S1. Obtain analytical calculation parameters of the target shield tunnel, analytical calculation parameters of the target shield soil, maximum allowable deformation and initial deformation of the target shield tunnel lining, surface cover load characteristics, and analytical calculation parameters of the water level;

[0007] S2. Constructing a first shield tunnel stress calculation model based on analytical calculation parameters of the target shield tunnel, analytical calculation parameters of the target shield soil, surface cover load characteristics, and analytical calculation parameters of the water level, and calculating additional stress at the axis of the target shield tunnel based on the first shield tunnel stress calculation model;

[0008] S3. Constructing an additional stress work equation at the target shield tunnel axis, and solving the additional stress work equation based on the additional stress at the target shield tunnel axis to obtain the total work done by the target shield tunnel under the force;

[0009] S4. Constructing a longitudinal deformation calculation model for the second shield tunnel based on the energy method, and solving the longitudinal deformation calculation model for the second shield tunnel based on the total work done by the target shield tunnel under the force to obtain a longitudinal displacement field at the axis of the target shield tunnel;

[0010] S5. Construct a third shield lining performance nonlinear degradation model based on the maximum allowable deformation and initial deformation of the target shield tunnel lining. Solve the third shield lining performance nonlinear degradation model according to the longitudinal displacement field at the axis of the target shield tunnel to obtain an evaluation index of the longitudinal deformation of the target shield tunnel.

[0011] S6. Evaluate the longitudinal deformation of the target shield tunnel based on the evaluation indicators.

[0012] Optionally, the analytical calculation parameters of the target shield tunnel in S1 include: the buried depth of the shield tunnel axis;

[0013] The analytical calculation parameters of the target shield soil include: soil Poisson's ratio and soil elastic modulus;

[0014] The surface cover load characteristics include: cover load weight, cover load length, cover load width and cover load depth;

[0015] Water level analysis calculation parameters include: initial water level height and dynamically changing water level height.

[0016] Optionally, the S2 includes:

[0017] A first shield tunnel stress calculation model is constructed based on the characteristics of the target shield tunnel to calculate the additional stress at the axis of the target shield tunnel, wherein the additional stress includes: stratum reaction force, external water pressure of the shield tunnel lining, and additional stress of the overburden load;

[0018] Substitute the analytical calculation parameters of the target shield tunnel, the analytical calculation parameters of the target shield soil, the surface cover load characteristics, and the analytical calculation parameters of the water level into the first shield tunnel stress calculation model to solve the ground reaction force at the target shield tunnel axis, the external water pressure on the shield tunnel lining, and the additional stress of the cover load. The first shield tunnel stress calculation model satisfies the following relationship:

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] Where: s q ( x ) is the vertical stress caused by the overburden load at a certain point on the tunnel axis, q is the cover load weight, which takes a negative value under loading conditions and a positive value under unloading conditions. R 1. R 2 are the distances from the load action point to the target point and the distances from its mirror image point about the ground to the target point, B is the width of the cover load, L is the topsoil cover load length, h is half the height of the cover load. P ( y , z ) is the water pressure at any position outside the lining, P r0 is the water pressure inside the lining, take 0, h w is the surface water head, c The tunnel depth, r is the lining radius, Z ( x ) is the foundation reaction force, w ( x ) is the foundation deformation, k is the foundation stiffness coefficient, g is the foundation shear coefficient, r g is the thickness of the grouting ring,k r , k g is the permeability coefficient of the formation and grouting circle, R ( x ) The total additional stress at a point on the tunnel axis, c w is the specific gravity of water, E S is the equivalent elastic modulus of the formation, IE is the segment stiffness, h 1 is the thickness of the shear layer, take 2.5 D , h 2 is the height of groundwater level after water level changes, D is the tunnel diameter, F t 、 F c 、 F s are the inter-ring tensile stress, inter-ring compressive stress, and inter-ring shear stress, respectively. c 1 is the natural weight of the soil, c 2 is the saturated density of soil, G is the weight per unit length of the segment, c c is the bulk density of the lining, r 0 is the inner diameter of the lining, k s is the shear stiffness between segments, k t is the tensile stiffness between segments, k c is the compressive stiffness between segments, i m is the angle between adjacent rings, Δ w m is the displacement between adjacent rings, i j For unit area P The angle with the vertical, x is the correction factor, k b 、 k s is the Timoshenko shear coefficient of the bolt and segment ring, l b is the length of the bolt, E b 、 E s is the elastic modulus of concrete and bolts, m b 、 m s is the Poisson's ratio of concrete to bolts,A b is the cross-sectional area of ​​a single bolt, n b is the number of bolts, A s is the cross-sectional area of ​​the segment concrete, k b is the average linear stiffness of the bolt, [ A ] is the intermediate parameter in the corresponding calculation formula, is the symbol of partial derivative, x is the longitudinal coordinate of the stress point to be sought, y is the transverse coordinate of the stress point to be sought, z is the vertical coordinate of the stress point to be sought, is the additional stress in the soil caused by water level changes, is the proportional coefficient of the tensile area between the two lining rings, is the vertical resultant force of the external water pressure on the lining, is the horizontal resultant force of the external water pressure on the lining, P is the external water pressure of the lining, m is the Poisson's ratio of soil, z 0 is the longitudinal coordinate of the stress point to be sought, h 0 is the ordinate of the vertical point load, Pv is the vertical resultant force of the external water pressure on the lining, y ( i j ) is the vertical coordinate representation in the form of spatial coordinates, z ( i j ) is the vertical coordinate representation in the form of spatial coordinates, s 1 is the total stress of the soil after the water level changes, u 1 is the pore water pressure of the soil after the water level changes, s 0 is the total stress of the soil under the initial water level, u 0 is the pore water pressure of the soil after the water level changes, r 1 is the outer diameter of the tunnel;

[0034] The above calculation formula obtained s q ( x ), Pv 、 Z ( x ), R ( x ), F t 、 F c 、 F s 、 G Both are the forces at the axis of the target shield tunnel.

[0035] Optionally, the S3 includes:

[0036] Based on the ground reaction force, the external water pressure of the shield tunnel lining, and the additional stress of the overburden load, the additional stress work equation is constructed. The additional stress work equation includes the work equation for overcoming the ground reaction force, the work equation for overcoming the inter-annular shear force, the work equation for overcoming the inter-annular tensile stress, and the work equation for the vertical component of the lining water pressure.

[0037] Based on the work equations for overcoming the ground reaction force, the work equations for overcoming the inter-ring shear force, the work equations for overcoming the inter-ring tensile stress, and the work equations for the vertical component of the lining water pressure, a calculation model for the total work done by the specific ring of the target shield tunnel is constructed. The ground reaction force, the external water pressure of the shield tunnel lining, and the additional stress of the cover load are substituted into the calculation model for the specific ring of the target shield tunnel to solve the total work done by the target shield tunnel. The calculation model for the total work done by the specific ring of the target shield tunnel satisfies the following relationship:

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] ;

[0047] Where: W R The work done for the additional stress, W k The work done to overcome the reaction force of the formation, W S To overcome the work done between rings, W t To overcome the tension between the rings, W c The work done to overcome the compressive stress between the rings is W P is the work done by the vertical water pressure outside the lining, W Gis the work done by the gravity of the lining ring, W is the total work done by the target shield tunnel force, N To calculate the number of segment rings taken, m Calculate the required number of segment rings.

[0048] Optionally, the S4 includes:

[0049] Based on the energy variation method and the minimum potential energy principle, a calculation model for the longitudinal deformation of the second shield tunnel is constructed. The total work done by the target shield tunnel under the force is substituted into the calculation model for the longitudinal deformation of the second shield tunnel to solve the longitudinal displacement field at the axis of the target shield tunnel. The calculation model for the longitudinal deformation of the second shield tunnel satisfies the following relationship:

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] ;

[0063] Where: K s ] is the stiffness matrix of the formation reaction force, [ K G ] is the gravity matrix, [ K t ] is the tunnel ring stiffness matrix, [ P ] T is the effect of water pressure on the tunnel lining ring, [ G ] T is the effect of gravity, [ s ′] T is the effect of additional formation stress caused by water level, [ R ] T is the interaction effect between the free displacement of soil and the tunnel lining ring, a n is the Fourier expansion coefficient, n is the number of Fourier expansion terms, T n ( x ) is the Fourier expansion matrix, A is the Fourier expansion coefficient matrix, x i is the number of different Fourier expansion terms, and T is the matrix transpose symbol.

[0064] Optionally, the S5 includes:

[0065] A nonlinear degradation model of the third shield lining performance is constructed. The longitudinal displacement field at the axis of the target shield tunnel is substituted into the nonlinear degradation model of the third shield lining performance to solve the lining structural performance. The lining structural performance is used as an evaluation index of the longitudinal deformation of the target shield tunnel. The nonlinear degradation model of the third shield lining performance satisfies the following relationship:

[0066] ;

[0067] Where: Q is the lining structure performance, Δ w max When the tunnel structure fails ( Q ( t )=0), the maximum allowable longitudinal deformation, Δ w 0 is the initial deformation, Δ w ( t ) is the longitudinal deformation output by the longitudinal deformation calculation model of the second shield tunnel.

[0068] Optionally, the S6 includes:

[0069] A preset index threshold is determined based on the construction characteristics of the target shield tunnel. When the evaluation index of the longitudinal deformation of the target shield tunnel is greater than or equal to the preset index threshold, the current lining structure performance is evaluated as high performance.

[0070] When the evaluation index of the longitudinal deformation of the target shield tunnel is less than the preset index threshold, but greater than or equal to 0.75 times the preset index threshold, the current lining structure performance is evaluated as medium performance;

[0071] When the evaluation index of the longitudinal deformation of the target shield tunnel is less than 0.75 times the preset index threshold, but greater than or equal to 0.5 times the preset index threshold, the current lining structure performance is evaluated as low performance;

[0072] When the evaluation index of the longitudinal deformation of the target shield tunnel is less than 0.5 times the preset index threshold, but greater than or equal to 0.25 times the preset index threshold, the current lining structure performance is evaluated as no performance;

[0073] And 0.25 times the preset indicator threshold is the indicator critical value with no performance, and the case where it is less than 0.25 times the preset indicator threshold is not evaluated.

[0074] In a second aspect, an embodiment of the present application provides a comprehensive evaluation system for longitudinal deformation of a shield tunnel, including a processor and a memory;

[0075] Memory for storing computer programs;

[0076] The processor is configured to implement any one of the method steps described in the first aspect when executing a program stored in the memory.

[0077] Beneficial effects:

[0078] The present invention provides a comprehensive evaluation method for the longitudinal deformation of a shield tunnel. The method constructs a force calculation model for the shield tunnel axis caused by water level changes and overburden loads based on the target shield tunnel, shield soil, maximum and initial allowable deformations of the shield tunnel lining, surface overburden load characteristics, and water level analytical calculation parameters, and calculates the forces on the shield tunnel. A control equation for the longitudinal deformation of the shield tunnel is then derived based on the energy variation method and the principle of minimum potential energy, taking into account the shear effect of the foundation. The performance of the shield tunnel lining is calculated based on the control equation for the longitudinal deformation of the shield tunnel and the established shield lining performance degradation model, and the performance is used as an evaluation indicator for the shield tunnel under the effects of water level changes and overburden loads.

[0079] It is worth noting that the present invention constructs a first shield tunnel force calculation model caused by water level changes and overburden loads, combines the energy variation method and the minimum potential energy principle to establish a second calculation model reflecting the longitudinal deformation of the shield tunnel, and then based on the longitudinal deformation of the shield tunnel of the second model and the third model of nonlinear degradation of the shield lining performance, obtains a highly innovative and overall systematic evaluation index of the shield tunnel under the action of water level changes and overburden loads. Compared with the finite element method, finite difference method, indoor model test and field test, this method is simpler, faster and more accurate, and has higher engineering application and promotion value. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 Flowchart of a comprehensive evaluation method for longitudinal deformation of a shield tunnel according to a preferred embodiment of the present invention;

[0081] Figure 2Schematic diagram of a calculation model for a comprehensive evaluation method of longitudinal deformation of a shield tunnel according to a preferred embodiment of the present invention, wherein (a) illustrates the physical and mechanical parameters of a shield tunnel under the action of foundation pit excavation, and (b) illustrates the physical and mechanical parameters of a shield tunnel under water level changes;

[0082] Figure 3 A diagram of the longitudinal force model of a shield tunnel provided in a preferred embodiment of the present invention;

[0083] Figure 4 A diagram of a lateral force model of a shield tunnel provided in a preferred embodiment of the present invention;

[0084] Figure 5 A schematic diagram of longitudinal deformation of a shield tunnel provided by a preferred embodiment of the present invention;

[0085] Figure 6 A schematic diagram of lining performance changes provided by a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0086] The following is a clear and complete description of the technical solutions of the present invention. It should be understood that the embodiments described are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0087] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "one" or "a" do not indicate a quantity limitation, but rather indicate the existence of at least one. Words such as "connected" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship also changes accordingly.

[0088] See Figure 1-6 The embodiment selected in this application provides a comprehensive evaluation method for longitudinal deformation of a shield tunnel, the specific steps are as follows: Figure 1 Shown, including:

[0089] Obtain the target shield tunnel, shield soil, shield tunnel lining maximum allowable and initial deformation, surface cover load characteristics, and water level analytical calculation parameters;

[0090] Based on the analytical calculation parameters, a first shield tunnel stress calculation model, a second shield tunnel longitudinal deformation calculation model, and a third shield tunnel lining performance nonlinear degradation model are constructed, wherein the first shield tunnel stress calculation model is used to calculate the additional stress at the shield tunnel axis caused by water level changes and overburden loads, the second shield tunnel longitudinal deformation calculation model is used to calculate the longitudinal deformation of the shield tunnel, and the third shield tunnel lining performance nonlinear degradation model is used to calculate the lining performance degradation caused by shield tunnel deformation;

[0091] Calculating the force at the axis of the shield tunnel based on the first shield tunnel force calculation model, calculating the longitudinal deformation at the axis of the shield tunnel based on the second shield tunnel longitudinal deformation calculation model, and calculating the shield tunnel lining performance based on the third shield tunnel lining performance nonlinear degradation model;

[0092] Based on the energy method, the shield tunnel longitudinal deformation control equation is derived and constructed, wherein the shield tunnel longitudinal deformation control equation is used to reflect the bending effect and shear effect of the stratum;

[0093] An analytical expression for the longitudinal deformation of the tunnel is constructed based on the tunnel longitudinal deformation control equation and the principle of minimum potential energy.

[0094] The performance of the shield tunnel segments is calculated based on the calculation results of the analytical formula of the tunnel longitudinal deformation and the third shield tunnel lining performance nonlinear degradation model, and the performance of the shield tunnel segments is used as an evaluation index of the shield tunnel.

[0095] In the above embodiment, a shield tunnel force calculation model is constructed by using the target shield tunnel, shield soil, maximum and initial allowable deformations of the shield tunnel lining, surface cover load characteristics, and water level analytical calculation parameters; then, a shield tunnel longitudinal deformation control equation is derived based on the energy method, wherein the shield tunnel longitudinal deformation control equation is used to reflect the bending effect and shear effect of the stratum, and an analytical expression reflecting the longitudinal deformation of the tunnel is constructed based on the tunnel longitudinal deformation control equation and the minimum potential energy principle; then, based on the energy variation method and the minimum potential energy principle, a shield tunnel longitudinal deformation control equation considering the foundation shear effect is derived; based on the shield tunnel longitudinal deformation control equation and the established shield tunnel lining degradation model, the performance of the shield tunnel lining is calculated, and the performance is used as an evaluation index of the shield tunnel under water level changes and cover loads.

[0096] The specific steps of its embodiment are as follows:

[0097] (1) Determine the analytical calculation parameters of the existing shield and soil under the action of water level changes and overburden loads.

[0098] like Figure 2 As shown in Figure 2, the physical and mechanical parameters of the shield tunnel under the influence of water level changes and foundation pit excavation in a certain project, among which, Figure 2 Figure (a) shows the physical and mechanical parameters of a shield tunnel under the action of foundation pit excavation. Under the action of foundation pit excavation, loads are applied to the surface and soil layer. The soil layer will be unloaded according to the applied loads. Under the action of loading and unloading, additional stress will be generated in the shield tunnel, causing tunnel uplift and settlement. Figure 2 (b) shows the physical and mechanical parameters of a shield tunnel under changing water levels. The rise and fall of water levels also generate additional stress on the shield tunnel, causing tunnel uplift and subsidence. The specific physical and mechanical parameters are as follows:

[0099] a) Shield tunnel: Shield segment weight 25 kN / m 3 , burial depth 6m, shield outer diameter 3m, shield inner diameter 2.7m, segment elastic modulus 3.45×10 4 MPa, segment shear modulus 14.375 MPa, segment bending stiffness 754.8 GPa, segment inter-ring tensile stiffness 9.28×10 4 MPa, inter-ring compressive stiffness 1.48×10 8 MPa, inter-ring tensile stiffness 3.06×10 6 MPa, Poisson's ratio 0.2; grouting layer density 22 kN / m 3 , the inner diameter of the grouting layer is 3.1m, and the inner diameter is 3m.

[0100] b) Cover load: width 10m, length 10m, depth 1m, cover load weight 18 kN / m 3 .

[0101] c) Soil parameters: elastic modulus 15 MPa, gravity 18 kN / m 3 , Poisson's ratio 0.3.

[0102] d) Water level: Water density 10 kN / m 3 , water level 12m.

[0103] e) Maximum allowable and initial deformation of shield tunnel lining: maximum allowable deformation 20mm, initial deformation 0.5mm.

[0104] After inputting the acquired parameters, the stress of the shield tunnel and the lining performance degradation model are first calculated. The calculated shield stress can be further used to calculate the total stress, and then the longitudinal deformation equation of the shield tunnel is established based on the energy method and the minimum potential energy principle, thereby obtaining the longitudinal displacement of the shield tunnel, and then the performance index of the lining is calculated based on the lining performance degradation model.

[0105] After obtaining the input parameters, the shield tunnel forces are first calculated. After calculating the shield forces, the total work done by the shield tunnel forces can be calculated. Then, based on the energy method and the principle of minimum potential energy, the governing equation for tunnel deformation is established to solve the shield tunnel deformation. Combined with the established lining performance degradation model, the lining performance is calculated and graded according to the lining performance.

[0106] Finally, the final segment performance and lining performance grade are output.

[0107] The parameters in the above embodiments are all calculated by constructing a shield tunnel mechanical model, a shield tunnel deformation model and a shield tunnel lining performance degradation model. The shield tunnel mechanical model analytical calculation model is as follows: Figure 3 、 Figure 4 As shown, Figure 3 This is the longitudinal stress model diagram of the shield tunnel. Figure 4 This is the lateral force model diagram of the shield tunnel.

[0108] In this embodiment, the specific values ​​of the parameters are for demonstration only and are not limiting.

[0109] Substituting the required calculation parameters into equations (1)-(13), the forces at the axis of the shield tunnel under the action of water level changes and overburden loads are calculated.

[0110] (1)

[0111] (2)

[0112] (3)

[0113] (4)

[0114] (5)

[0115] (6)

[0116] (7)

[0117] (8)

[0118] (9)

[0119] (10)

[0120] (11)

[0121] (12)

[0122] (13)

[0123] Where: s q ( x ) is the vertical stress caused by the overburden load at a certain point on the tunnel axis; q is the weight of the cover load, which takes a negative value under loading conditions and a positive value under unloading conditions; R 1. R 2 are the distances from the load action point to the target point and from its mirror image point about the ground to the target point, respectively, and , ; B is the width of cover load; L is the topsoil cover load length; h Half of the cover load height; P ( y , z ) is the water pressure at any position outside the lining; P r0 is the water pressure inside the lining, which is taken as 0; h w is the surface water head; c The depth of the tunnel; r is the lining radius; Z ( x ) is the foundation reaction; w ( x ) is foundation deformation; k is the foundation stiffness coefficient; G is the foundation shear coefficient; r g is the thickness of the grouting ring; k r , k g is the permeability coefficient of the formation and grouting circle; R ( x ) the total additional stress at a point on the tunnel axis; c w is the bulk density of water; E S is the equivalent elastic modulus of the formation; IE is the segment stiffness; h 1 is the thickness of the shear layer, take 2.5 D , D is the tunnel diameter; F t 、 F c 、 F s They are inter-ring tensile stress, inter-ring compressive stress, and inter-ring shear stress respectively; c1 is the natural density of soil; c 2 is the saturated density of soil; G is the weight per unit length of the segment; c c is the bulk density of the lining; r 0 is the inner diameter of the lining; k s is the shear stiffness between segments; k t is the tensile stiffness between segments; k c is the compressive stiffness between segments; i m is the angle between adjacent rings; Δ w m is the displacement between adjacent rings; i j For unit area P Angle with vertical; x is the correction factor; k b 、 k s is the Timoshenko shear coefficient of the bolt and segment ring; l b is the length of the bolt; E b 、 E s is the elastic modulus of concrete and bolts; m b 、 m s is the Poisson's ratio of concrete to bolts; A b is the cross-sectional area of ​​a single bolt; n b is the number of bolts; A s is the cross-sectional area of ​​the segment concrete; k b is the average linear stiffness of the bolt; [ A ] is the intermediate parameter in the corresponding calculation formula.

[0124] In the above calculations, the vertical stress formula for the overburden load and the foundation reaction formula are combined with tunnel burial depth, soil parameters such as Poisson's ratio and elastic modulus, overburden load parameters such as density, width, and depth, and water level parameters such as head height and dynamic changes to calculate the ground reaction force, external water pressure, and additional stress due to the overburden load. Through the above force calculations, multiple factors such as overburden load, water pressure, and foundation shear effect can be fully incorporated, avoiding the limitations of a simplified model based on a single factor. At the same time, the foundation reaction formula, combined with stiffness and shear coefficient, more realistically reflects the interaction between the soil and the tunnel, improving the physical rationality of the additional stress calculation.

[0125] Substitute the tunnel forces calculated above into equations (14)-(22)

[0126] (14)

[0127] (15)

[0128] (16)

[0129] (17)

[0130] (18)

[0131] (19)

[0132] (20)

[0133] (twenty one)

[0134] (twenty two)

[0135] Where: W R the work done for the additional stress; W Z The work done to overcome the reaction force of the formation; W S The work done to overcome the inter-ring buildup; W t The work done to overcome the tension between the rings; W c The work done to overcome the compressive stress between the rings; W P The work done by the vertical water pressure outside the lining; W G The work done by the gravity of the lining ring; N In order to calculate the number of segment rings, in this example N Take 60.

[0136] In the above calculations, by constructing a work equation to overcome the formation reaction force, inter-annular shear force, tensile stress, and water pressure components, and by superimposing the work of each component, the total work W can be obtained. Through the above work calculation, the complex force is converted into energy form, providing input for the subsequent energy method and ensuring the strict application of the principle of conservation of energy. At the same time, through the quantification of the component work, the contribution weight of each factor to the total deformation is clarified, facilitating targeted optimization design.

[0137] After calculating the total work done by the tunnel force, based on the energy method and the principle of minimum potential energy, the assumed tunnel deformation equation is substituted into the energy equation to obtain the control equation for the longitudinal deformation of the tunnel. The calculation formulas are shown in Equations (23)-(36):

[0138] (twenty three)

[0139] (twenty four)

[0140] (25)

[0141] (26)

[0142] (27)

[0143] (28)

[0144] (29)

[0145] (30)

[0146] (31)

[0147] (32)

[0148] (33)

[0149] (34)

[0150] (35)

[0151] (36)

[0152] Where: K s ] is the stiffness matrix of the formation reaction force, [ K t ]Tunnel ring stiffness matrix,[ P ] Tis the effect of water pressure on the tunnel lining ring, [ G ] T is the effect of gravity, [ s ′] T is the effect of additional formation stress caused by water level, [ R ] T is the interaction effect between the free displacement of soil and the tunnel lining ring.

[0153] In the above calculations, based on the energy variation method and the principle of minimum potential energy, the stiffness matrix and Fourier expansion are constructed to solve the longitudinal displacement field. The total work and the Fourier coefficient matrix are combined to analyze the longitudinal deformation distribution of the tunnel. Through the above calculation of the displacement field, the continuum problem is discretized into a matrix equation, simplifying the computational complexity and improving the efficiency of the numerical solution. At the same time, the stiffness matrix can reflect the coupling effects of different deformation modes (such as bending and shear), accurately capturing the spatial distribution characteristics of tunnel deformation.

[0154] According to the above calculation, the longitudinal deformation of the tunnel can be obtained, such as Figure 5 As shown, Figure 5 Schematic diagram of longitudinal deformation of shield tunnel. Figure 5 The tunnel settlement distance caused by the longitudinal deformation of the middle tunnel can be calculated by the above formula. The performance of the lining can be calculated by formula (37) and the performance grade can be rated.

[0155] (37)

[0156] Where: Q is the lining structure performance, Δ w max When the tunnel structure fails ( Q ( t )=0), the maximum allowable longitudinal deformation is 20mm; Δ w 0 is the initial deformation, which is 0.5mm; Δ w ( t ) is the longitudinal deformation output by the longitudinal deformation calculation model of the second shield tunnel.

[0157] Among them, the lining performance of the third shield tunnel obtained by the nonlinear degradation model meets the following indicators: Q 0. Q 1=0.75 Q 0. Q 2=0.50 Q 0. Q 3=0.25 Q 0, respectively meet the critical values ​​of high performance, medium performance, low performance, and no performance. The performance index result diagram is as follows Figure 6 As shown, Figure 6Schematic diagram of lining performance change. The lining performance obtained by calculation Q The larger it is, the higher the structural performance of the shield tunnel.

[0158] In the above calculations, quantifying lining performance through nonlinear formulas can make the nonlinear model more consistent with actual material degradation laws (such as concrete cracking and joint failure), avoiding errors in linear assumptions. At the same time, the normalized index Q can intuitively reflect the degree of structural performance degradation, providing a quantitative basis for maintenance decisions.

[0159] The embodiment of the present application also provides a comprehensive evaluation system for longitudinal deformation of a shield tunnel, comprising a processor and a memory;

[0160] Memory for storing computer programs;

[0161] The processor is used to implement any method step of the comprehensive evaluation method for longitudinal deformation of a shield tunnel when executing the program stored in the memory.

[0162] The above-mentioned comprehensive evaluation system for longitudinal deformation of a shield tunnel can implement various embodiments of the above-mentioned comprehensive evaluation method for longitudinal deformation of a shield tunnel and achieve the same beneficial effects, which will not be described in detail here.

[0163] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A comprehensive evaluation method for longitudinal deformation of a shield tunnel, characterized in that: include: S1. Obtain analytical calculation parameters of the target shield tunnel, analytical calculation parameters of the target shield soil, maximum allowable deformation and initial deformation of the target shield tunnel lining, surface cover load characteristics, and analytical calculation parameters of the water level; S2. Constructing a first shield tunnel stress calculation model based on analytical calculation parameters of the target shield tunnel, analytical calculation parameters of the target shield soil, surface cover load characteristics, and analytical calculation parameters of the water level, and calculating additional stress at the axis of the target shield tunnel based on the first shield tunnel stress calculation model; S3. Constructing an additional stress work equation at the target shield tunnel axis, and solving the additional stress work equation based on the additional stress at the target shield tunnel axis to obtain the total work done by the target shield tunnel under the force; S4. Constructing a longitudinal deformation calculation model for the second shield tunnel based on the energy method, and solving the longitudinal deformation calculation model for the second shield tunnel based on the total work done by the target shield tunnel under the force to obtain a longitudinal displacement field at the axis of the target shield tunnel; S5. Construct a third shield lining performance nonlinear degradation model based on the maximum allowable deformation and initial deformation of the target shield tunnel lining. Solve the third shield lining performance nonlinear degradation model according to the longitudinal displacement field at the axis of the target shield tunnel to obtain an evaluation index of the longitudinal deformation of the target shield tunnel. S6. Evaluate the longitudinal deformation of the target shield tunnel based on the evaluation index; Wherein, the S2 includes: A first shield tunnel stress calculation model is constructed based on the characteristics of the target shield tunnel to calculate the additional stress at the axis of the target shield tunnel, wherein the additional stress includes: stratum reaction force, external water pressure of the shield tunnel lining, and additional stress of the overburden load; Substitute the analytical calculation parameters of the target shield tunnel, the analytical calculation parameters of the target shield soil, the surface cover load characteristics, and the analytical calculation parameters of the water level into the first shield tunnel stress calculation model to solve the ground reaction force at the target shield tunnel axis, the external water pressure on the shield tunnel lining, and the additional stress of the cover load. The first shield tunnel stress calculation model satisfies the following relationship: ； ； ； ； ； ； ； ； ； ； ； ； ； ； Where: σ q ( x ) is the vertical stress caused by the overburden load at a certain point on the tunnel axis, q is the cover load weight, which takes a negative value under loading conditions and a positive value under unloading conditions. R 1. R 2 are the distances from the load action point to the target point and the distances from its mirror image point about the ground to the target point, B is the width of the cover load, L is the topsoil cover load length, h is half the height of the cover load. P ( y , z ) is the water pressure at any position outside the lining, P r0 is the water pressure inside the lining, take 0, h w is the surface water head, c The tunnel depth, r is the lining radius, Z ( x ) is the foundation reaction force, w ( x ) is the foundation deformation, k is the foundation stiffness coefficient, g is the foundation shear coefficient, r g is the thickness of the grouting ring, k r , k g is the permeability coefficient of the formation and grouting circle, R ( x ) The total additional stress at a point on the tunnel axis, γ w is the specific gravity of water, E S is the equivalent elastic modulus of the formation, EI is the segment stiffness, h 1 is the thickness of the shear layer, take 2.5 D , h 2 is the height of groundwater level after water level changes, D is the tunnel diameter, F t 、 F c 、 F s are the inter-ring tensile stress, inter-ring compressive stress, and inter-ring shear stress, respectively. γ 1 is the natural weight of the soil, γ 2 is the saturated density of soil, G is the weight per unit length of the segment, γ c is the bulk density of the lining, r 0 is the inner diameter of the lining, k s is the shear stiffness between segments, k t is the tensile stiffness between segments, k c is the compressive stiffness between segments, θ m is the angle between adjacent rings, Δ w m is the displacement between adjacent rings, θ j For unit area P The angle with the vertical, ξ is the correction factor, κ b 、 κ s is the Timoshenko shear coefficient of the bolt and segment ring, l b is the length of the bolt, E b 、 E s is the elastic modulus of concrete and bolts, μ b 、 μ s is the Poisson's ratio of concrete to bolts, A b is the cross-sectional area of ​​a single bolt, n b is the number of bolts, A s is the cross-sectional area of ​​the segment concrete, k b is the average linear stiffness of the bolt, [ A ] is the intermediate parameter in the corresponding calculation formula, is the symbol of partial derivative, x is the longitudinal coordinate of the stress point to be sought, y is the transverse coordinate of the stress point to be sought, z is the vertical coordinate of the stress point to be sought, is the additional stress in the soil caused by water level changes, is the proportional coefficient of the tensile area between the two lining rings, is the vertical resultant force of the external water pressure on the lining, is the horizontal resultant force of the external water pressure on the lining, P is the external water pressure of the lining, μ is the Poisson's ratio of soil, z 0 is the longitudinal coordinate of the stress point to be sought, h 0 is the ordinate of the vertical point load, Pv is the vertical resultant force of the external water pressure on the lining, y ( θ j ) is the vertical coordinate representation in the form of spatial coordinates, z ( θ j ) is the vertical coordinate representation in the form of spatial coordinates, σ 1 is the total stress of the soil after the water level changes, u 1 is the pore water pressure of the soil after the water level changes, σ 0 is the total stress of the soil under the initial water level, u 0 is the pore water pressure of the soil after the water level changes, r 1 is the outer diameter of the tunnel; The above calculation formula obtained σ q ( x ), Pv 、 Z ( x ), R ( x ), F t 、 F c 、 F s 、 G Both are the forces at the axis of the target shield tunnel.

2. The comprehensive evaluation method for longitudinal deformation of a shield tunnel according to claim 1, characterized in that: The analytical calculation parameters of the target shield tunnel in S1 include: the buried depth of the shield tunnel axis; The analytical calculation parameters of the target shield soil include: soil Poisson's ratio and soil elastic modulus; The surface cover load characteristics include: cover load weight, cover load length, cover load width and cover load depth; Water level analysis calculation parameters include: initial water level height and dynamically changing water level height.

3. The comprehensive evaluation method for longitudinal deformation of a shield tunnel according to claim 2, characterized in that: The S3 includes: Based on the ground reaction force, the external water pressure of the shield tunnel lining, and the additional stress of the overburden load, the additional stress work equation is constructed. The additional stress work equation includes the work equation for overcoming the ground reaction force, the work equation for overcoming the inter-annular shear force, the work equation for overcoming the inter-annular tensile stress, and the work equation for the vertical component of the lining water pressure. Based on the work equations for overcoming the ground reaction force, the work equations for overcoming the inter-ring shear force, the work equations for overcoming the inter-ring tensile stress, and the work equations for the vertical component of the lining water pressure, a calculation model for the total work done by the specific ring of the target shield tunnel is constructed. The ground reaction force, the external water pressure of the shield tunnel lining, and the additional stress of the cover load are substituted into the calculation model for the specific ring of the target shield tunnel to solve the total work done by the target shield tunnel. The calculation model for the total work done by the specific ring of the target shield tunnel satisfies the following relationship: ； ； ； ； ； ； ； ； ； Where: W R The work done for the additional stress, W k The work done to overcome the reaction force of the formation, W S To overcome the work done between rings, W t To overcome the tension between the rings, W c The work done to overcome the inter-ring compressive stress is W P is the work done by the vertical water pressure outside the lining, W G is the work done by the gravity of the lining ring, W is the total work done by the target shield tunnel force, N To calculate the number of segment rings taken, m Calculate the required number of segment rings.

4. The comprehensive evaluation method for longitudinal deformation of a shield tunnel according to claim 3, characterized in that: The S4 includes: Based on the energy variation method and the minimum potential energy principle, a calculation model for the longitudinal deformation of the second shield tunnel is constructed. The total work done by the target shield tunnel under the force is substituted into the calculation model for the longitudinal deformation of the second shield tunnel to solve the longitudinal displacement field at the axis of the target shield tunnel. The calculation model for the longitudinal deformation of the second shield tunnel satisfies the following relationship: ； ； ； ； ； ； ； ； ； ； ； ； ； Where: K s ] is the stiffness matrix of the formation reaction force, [ K G ] is the gravity matrix, [ K t ] is the tunnel ring stiffness matrix, [ P ] T is the effect of water pressure on the tunnel lining ring, [ G ] T is the effect of gravity, [ σ ′] T is the effect of additional formation stress caused by water level, [ R ] T is the interaction effect between the free displacement of soil and the tunnel lining ring, a n is the Fourier expansion coefficient, n is the number of Fourier expansion terms, T n ( x ) is the Fourier expansion matrix, A is the Fourier expansion coefficient matrix, ξ i is the number of different Fourier expansion terms, and T is the matrix transpose symbol.

5. The comprehensive evaluation method for longitudinal deformation of a shield tunnel according to claim 4, characterized in that: The S5 includes: A nonlinear degradation model of the third shield lining performance is constructed. The longitudinal displacement field at the axis of the target shield tunnel is substituted into the nonlinear degradation model of the third shield lining performance to solve the lining structural performance. The lining structural performance is used as an evaluation index of the longitudinal deformation of the target shield tunnel. The nonlinear degradation model of the third shield lining performance satisfies the following relationship: ； Where: Q is the lining structure performance, Δ w max When the tunnel structure fails ( Q ( t )=0), the maximum allowable longitudinal deformation, Δ w 0 is the initial deformation, Δ w ( t ) is the longitudinal deformation output by the longitudinal deformation calculation model of the second shield tunnel.

6. The comprehensive evaluation method for longitudinal deformation of a shield tunnel according to any one of claims 1 to 5, characterized in that: The S6 includes: A preset index threshold is determined based on the construction characteristics of the target shield tunnel. When the evaluation index of the longitudinal deformation of the target shield tunnel is greater than or equal to the preset index threshold, the current lining structure performance is evaluated as high performance. When the evaluation index of the longitudinal deformation of the target shield tunnel is less than the preset index threshold, but greater than or equal to 0.75 times the preset index threshold, the current lining structure performance is evaluated as medium performance; When the evaluation index of the longitudinal deformation of the target shield tunnel is less than 0.75 times the preset index threshold, but greater than or equal to 0.5 times the preset index threshold, the current lining structure performance is evaluated as low performance; When the evaluation index of the longitudinal deformation of the target shield tunnel is less than 0.5 times the preset index threshold, but greater than or equal to 0.25 times the preset index threshold, the current lining structure performance is evaluated as no performance; And 0.25 times the preset indicator threshold is the indicator critical value with no performance, and the case where it is less than 0.25 times the preset indicator threshold is not evaluated.

7. A comprehensive evaluation system for longitudinal deformation of a shield tunnel, characterized in that: Including processor and memory; Memory for storing computer programs; A processor, configured to implement the method steps described in any one of claims 1 to 6 when executing a program stored in a memory.

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